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From Physical Concept To Mathematical Structure
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Author :Lynn E. H. Trainor Publisher :Toronto ; Buffalo : University of Toronto Press ISBN 13 : Total Pages :428 pages Book Rating :4.:/5 (45 download)
Book Synopsis From Physical Concept to Mathematical Structure by : Lynn E. H. Trainor
Download or read book From Physical Concept to Mathematical Structure written by Lynn E. H. Trainor and published by Toronto ; Buffalo : University of Toronto Press. This book was released on 1979 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis New Foundations for Physical Geometry by : Tim Maudlin
Download or read book New Foundations for Physical Geometry written by Tim Maudlin and published by . This book was released on 2014-02 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tim Maudlin sets out a completely new method for describing the geometrical structure of spaces, and thus a better mathematical tool for describing and understanding space-time. He presents a historical review of the development of geometry and topology, and then his original Theory of Linear Structures.
Author :Lynn E. H. Trainor Publisher :Toronto ; Buffalo : University of Toronto Press ISBN 13 : Total Pages :428 pages Book Rating :4.:/5 (89 download)
Book Synopsis From Physical Concept to Mathematical Structure by : Lynn E. H. Trainor
Download or read book From Physical Concept to Mathematical Structure written by Lynn E. H. Trainor and published by Toronto ; Buffalo : University of Toronto Press. This book was released on 1979 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Physics for Mathematicians by : Michael Spivak
Download or read book Physics for Mathematicians written by Michael Spivak and published by . This book was released on 2010 with total page 733 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Structures of Mathematical Physics by : Steven P. Starkovich
Download or read book The Structures of Mathematical Physics written by Steven P. Starkovich and published by Springer Nature. This book was released on 2021 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook serves as an introduction to groups, rings, fields, vector and tensor spaces, algebras, topological spaces, differentiable manifolds and Lie groups --- mathematical structures which are foundational to modern theoretical physics. It is aimed primarily at undergraduate students in physics and mathematics with no previous background in these topics. Applications to physics --- such as the metric tensor of special relativity, the symplectic structures associated with Hamilton's equations and the Generalized Stokes's Theorem --- appear at appropriate places in the text. Worked examples, end-of-chapter problems (many with hints and some with answers) and guides to further reading make this an excellent book for self-study. Upon completing this book the reader will be well prepared to delve more deeply into advanced texts and specialized monographs in theoretical physics or mathematics.
Book Synopsis Lectures on Quantum Theory by : C. J. Isham
Download or read book Lectures on Quantum Theory written by C. J. Isham and published by Imperial College Press. This book was released on 1995-01-01 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on material taught to final-year physics undergraduates as part of the theoretical physics option at Imperial College. After a self-contained introduction to the essential ideas of vector spaces and linear operators, a bridge is built between the concepts and mathematics of classical physics, and the new mathematical framework employed in quantum mechanics. The axioms of nonrelativistic quantum theory are introduced, and shown to lead to a variety of new conceptual problems. Subjects discussed include state-vector reduction, the problem of measurement, quantum entanglement, the Kochen-Specker theorem, and the Bell inequalities. The book includes twenty-five problems with worked solutions. In the US it could serve as an excellent supplement for an introductory graduate course on quantum mechanics ... The discursive style and clear exposition make for equally attractive reading by someone familiar with the subject or by a student with only rudimentary knowledge .... The main text is supplemented by a substantial number of problems with solutions, which should help the beginner master the mathematics .. I would strongly recommend that anyone teaching the subject use this little book as supplementary reading". Physics Today (USA), Aug 1996 "The proper role of mathematics is to make things easy. When something can be expressed in the precise language of mathematics, results can be obtained by the application of given rules. Calculations are so simple that even computers can do them. Chris Isham's lectures on the mathematical and structural foundations of quantum theory, reproduced in this book, provide an excellent illustration of this truth ... a welcome addition tothe modern literature on quantum theory ... It is good to have a book that gives such an excellent description of the mathematical structure of quantum theory ..". Times Higher Educational Supp. (UK), 1996
Book Synopsis Lectures On Quantum Theory: Mathematical And Structural Foundations by : Isham Chris J
Download or read book Lectures On Quantum Theory: Mathematical And Structural Foundations written by Isham Chris J and published by World Scientific. This book was released on 1995-09-01 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on material taught to final-year physics undergraduates as part of the theoretical physics option at Imperial College. After a self-contained introduction to the essential ideas of vector spaces and linear operators, a bridge is built between the concepts and mathematics of classical physics, and the new mathematical framework employed in quantum mechanics. The axioms of nonrelativistic quantum theory are introduced, and shown to lead to a variety of new conceptual problems. Subjects discussed include state-vector reduction, the problem of measurement, quantum entanglement, the Kochen-Specker theorem, and the Bell inequalities. The book includes twenty-five problems with worked solutions.
Book Synopsis Physical Geometry by : Gustavo R Gonz Lez-Mart N
Download or read book Physical Geometry written by Gustavo R Gonz Lez-Mart N and published by CreateSpace. This book was released on 2011-09-24 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is generally recognized that there exist problems in Physics. In particular, A. Einstein remained critical of some theoretical ideas in modern physics until his death. He was unsatisfied with his own gravitation and advocated the need for a fundamental unified theory which would include relativity, electromagnetism and gravitation from the beginning. He stated that the concepts of parallelism and differentiation are important. Furthermore, present models for Particle Physics are expressed in terms of a very large number of empirical parameters and a high number of dimensions. They are not clearly related to a fundamental underlying physical interaction. Gravitation and Electrodynamics are faced with serious theoretical challenges, particularly in Cosmic Physics due to the possible existence of dark matter and energy. Differential geometry offers the appropriate mathematical structure to accomplish Einstein's physical ideas. The key is "how to differentiate." In the book we use an Ehresmann connection, a concept related to groups. The group is determined from electrodynamics and relativity as the automorphisms of the space-time geometric algebra. Matter and fields are represented by generator-valued tensors. Unification is given by the fundamental nonlinear equation associated to the group. Microscopic physics is the study of linear excitations, which are group representations characterized by discrete numbers. Results obtained indicate that gravitation and electromagnetism are unified in a nontrivial manner. Odd generators represent non classical interactions. The equation of motion determines a geodesic motion with the Lorentz force term. The Einstein field equation with a purely geometric energy momentum tensor is obtained. In the newtonian limit, the constant geometric energy density of a hyperbolic symmetric solution is related to the gravitational constant G. Far from the limit the parameter G would be variable. This effect may be interpreted as dark matter. In vacuum, the known gravitational solutions are obtained. Electromagnetism is related to an SU(2) subgroup. If we restrict to the even U(1) subgroup we obtain Maxwell's equations. The equation of motion is a geometric generalization of Dirac's equation. This geometry is the germ of quantum physics including its probabilistic aspects. The geometric nature of Planck's constant h and of light speed c is determined by their relations to the connection and the metric. The alpha coupling constant is also determined geometrically. Mass is defined in terms of energy. The geometry shows various physical triple structures. The geometric excitations have quanta of charge, flux and spin which determine the fractional quantum Hall effect. The bare-mass quotients of the three stable particles are calculated giving a geometric expression for the proton-electron mass ratio, previously known but physically unexplained. There are connection excitations whose masses correspond to the weak boson masses and allow a geometric interpretation of Weinberg's angle. The equation of motion determines the anomalous bare magnetic moments of the proton, the electron and the neutron. The "strong" electromagnetic odd SU(2) part, generates short range attractive magnetic potentials which are sufficiently strong to determine the binding energy of the deuteron and other light nuclides. The bare masses of the leptons in the three families are calculated as topological excitations of the electron. The masses of these excitations increase under the action of a strong connection and are related to meson and quark masses. The mass spectrum for low masses agrees with the physical particle mass spectrum. The proton shows a triple structure that may be related to a quark structure. The combinations of the three fundamental geometric excitations (proton, electron and neutrino) form other excitations and may be used to represent particles showing a symmetry under the group SU(3)xSU(2)XU(1).
Book Synopsis Mathematical Physics by : Robert Geroch
Download or read book Mathematical Physics written by Robert Geroch and published by University of Chicago Press. This book was released on 2015-08-01 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Physics is an introduction to such basic mathematical structures as groups, vector spaces, topological spaces, measure spaces, and Hilbert space. Geroch uses category theory to emphasize both the interrelationships among different structures and the unity of mathematics. Perhaps the most valuable feature of the book is the illuminating intuitive discussion of the "whys" of proofs and of axioms and definitions. This book, based on Geroch's University of Chicago course, will be especially helpful to those working in theoretical physics, including such areas as relativity, particle physics, and astrophysics.
Book Synopsis Space, Time, Matter by : Hermann Weyl
Download or read book Space, Time, Matter written by Hermann Weyl and published by Courier Corporation. This book was released on 1952-01-01 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The standard treatise on the general theory of relativity." — Nature "Whatever the future may bring, Professor Weyl's book will remain a classic of physics." — British Journal for Philosophy and Science Reflecting the revolution in scientific and philosophic thought which accompanied the Einstein relativity theories, Dr. Weyl has probed deeply into the notions of space, time, and matter. A rigorous examination of the state of our knowledge of the world following these developments is undertaken with this guiding principle: that although further scientific thought may take us far beyond our present conception of the world, we may never again return to the previous narrow and restricted scheme. Although a degree of mathematical sophistication is presupposed, Dr. Weyl develops all the tensor calculus necessary to his exposition. He then proceeds to an analysis of the concept of Euclidean space and the spatial conceptions of Riemann. From this the nature of the amalgamation of space and time is derived. This leads to an exposition and examination of Einstein's general theory of relativity and the concomitant theory of gravitation. A detailed investigation follows devoted to gravitational waves, a rigorous solution of the problem of one body, laws of conservation, and the energy of gravitation. Dr. Weyl's introduction of the concept of tensor-density as a magnitude of quantity (contrasted with tensors which are considered to be magnitudes of intensity) is a major step toward a clearer understanding of the relationships among space, time, and matter.
Book Synopsis A New Foundation of Physical Theories by : Günther Ludwig
Download or read book A New Foundation of Physical Theories written by Günther Ludwig and published by Springer Science & Business Media. This book was released on 2007-06-07 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aims to clarify and formulate the fundamental ideas of physical theories. Suitable for both physicists and philosophers of science, this book introduces the concept of idealization and reviews the process of discovering new concepts.
Book Synopsis Geometric Structures in Nonlinear Physics by : Robert Hermann
Download or read book Geometric Structures in Nonlinear Physics written by Robert Hermann and published by Math Science Press. This book was released on 1991 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: VOLUME 26 of INTERDISCIPLINARY MATHEMATICS, series expounding mathematical methodology in Physics & Engineering. TOPICS: Differential & Riemannian Geometry; Theories of Vorticity Dynamics, Einstein-Hilbert Gravitation, Colobeau-Rosinger Generalized Function Algebra, Deformations & Quantum Mechanics of Particles & Fields. Ultimate goal is to develop mathematical framework for reconciling Quantum Mechanics & concept of Point Particle. New ideas for researchers & students. Order: Math Sci Press, 53 Jordan Road, Brookline, MA 02146. (617) 738-0307.
Book Synopsis Structure and Approximation in Physical Theories by : A. Hartkamper
Download or read book Structure and Approximation in Physical Theories written by A. Hartkamper and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume contains 14 contributions presented at a colloquium on "Structure and Approximation in Physical Theories" held at Osnabruck in June 1980. The articles are presented in the revised form written after the colloquium and hence also take account of the results of the discussion at the colloquium. It is a striking feature that the problem of approximation in physical theories has only recently found some attention in the philosophy of science, although the working physicist is con stantly confronted with those questions. No interesting theory of exact science exactly fits its experimental data; almost every relation between different theories is an approximate one. There fore an adequate reconstruction of physical theories must take into account and conceptualize the moment of approximation. The majority of the articles in this book is centered around this subject. There are at least two elaborate, 'structuralistic' approaches to the formalization of physical theories in which the aspect of approximation has been incorporated: the approach due to P. Suppes, J. Sneed, W. Stegmuller ("S-approach") and the approach of G. Lud wig and his co-workers ("L-approach"). The articles in this book correspondingly fall into three classes: presentation, elaboration and critique of the L-approach [Hartkamper/Schmidt, Ludwig, Neumann, Werner, Schmidt, Mayr, Kamiah, Majer, Grafe] or of the S-approach [Moulines, Balzer, Cooke], and articles referring to both approaches or concerned with related matters [Scheibe, Pfarr, Castrigiano]. Of course, this is only a rough classification and each article must be appraised in its own right.
Book Synopsis Mathematics, Ideas and the Physical Real by : Albert Lautman
Download or read book Mathematics, Ideas and the Physical Real written by Albert Lautman and published by A&C Black. This book was released on 2011-06-02 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: Albert Lautman (1908-1944) was a French philosopher of mathematics whose work played a crucial role in the history of contemporary French philosophy. His ideas have had an enormous influence on key contemporary thinkers including Gilles Deleuze and Alain Badiou, for whom he is a major touchstone in the development of their own engagements with mathematics. Mathematics, Ideas and the Physical Real presents the first English translation of Lautman's published works between 1933 and his death in 1944. Rather than being preoccupied with the relation of mathematics to logic or with the problems of foundation, which have dominated philosophical reflection on mathematics, Lautman undertakes to develop an understanding of the broader structure of mathematics and its evolution. The two powerful ideas that are constants throughout his work, and which have dominated subsequent developments in mathematics, are the concept of mathematical structure and the idea of the essential unity underlying the apparent multiplicity of mathematical disciplines. This collection of his major writings offers readers a much-needed insight into his influence on the development of mathematics and philosophy.
Book Synopsis Our Mathematical Universe by : Max Tegmark
Download or read book Our Mathematical Universe written by Max Tegmark and published by Vintage. This book was released on 2015-02-03 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: Max Tegmark leads us on an astonishing journey through past, present and future, and through the physics, astronomy and mathematics that are the foundation of his work, most particularly his hypothesis that our physical reality is a mathematical structure and his theory of the ultimate multiverse. In a dazzling combination of both popular and groundbreaking science, he not only helps us grasp his often mind-boggling theories, but he also shares with us some of the often surprising triumphs and disappointments that have shaped his life as a scientist. Fascinating from first to last—this is a book that has already prompted the attention and admiration of some of the most prominent scientists and mathematicians.
Book Synopsis A Mathematical Structure for Emergent Computation by : Victor Korotkikh
Download or read book A Mathematical Structure for Emergent Computation written by Victor Korotkikh and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: An understanding of emergent computation requires a profound revision of the most fundamental ideas. A noticeable attempt of such a rethinking is a world view in which natural systems are seen not as separate entities but as integrated parts of a unified whole. The book for the first time presents such a mathematical structure, which remarkably is based on integers as the single concept. As integers are considered to be the most fundamental entities irreducible to something simpler, this makes the mathematical structure a final theory, and thus we do not have to look for its explanation in terms of deeper concepts. The book is not only applicable to models of computation and optimization but also has scientific consequences, as it contributes to a rethinking of the most fundamental ideas about nature. Audience: The book is written at a level suitable for advanced undergraduate students and graduate students as well as research workers and practitioners in computer science information technology, mathematics and physics. The book is suitable as a reference or as supplementary reading material for an advanced graduate course. Only a basic knowledge of calculus is required.
Book Synopsis The Logical Structure of Mathematical Physics by : J.D. Sneed
Download or read book The Logical Structure of Mathematical Physics written by J.D. Sneed and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about scientific theories of a particular kind - theories of mathematical physics. Examples of such theories are classical and relativis tic particle mechanics, classical electrodynamics, classical thermodynamics, statistical mechanics, hydrodynamics, and quantum mechanics. Roughly, these are theories in which a certain mathematical structure is employed to make statements about some fragment of the world. Most of the book is simply an elaboration of this rough characterization of theories of mathematical physics. It is argued that each theory of mathematical physics has associated with it a certain characteristic mathematical struc ture. This structure may be used in a variety of ways to make empirical claims about putative applications of the theory. Typically - though not necessarily - the way this structure is used in making such claims requires that certain elements in the structure play essentially different roles. Some playa "theoretical" role; others playa "non-theoretical" role. For example, in classical particle mechanics, mass and force playa theoretical role while position plays a non-theoretical role. Some attention is given to showing how this distinction can be drawn and describing precisely the way in which the theoretical and non-theoretical elements function in the claims of the theory. An attempt is made to say, rather precisely, what a theory of mathematical physics is and how you tell one such theory from anothe- what the identity conditions for these theories are.
